Why does my displacement map have jaggies
First in first, EEVEE is not ready for fully support of displacement in 2.81 and below.

The node connect to displacement socket will become bump only solution. And there doesn't exist the displacement setting block inside the material panel with EEVEE. When you switch back to cycle, you can choose the type of displacement.



Using cubic interpolation might get the best result in cycles



Once upon user zoom-in into a ridiculous close place to look into mesh, linear method will become pixelated for some reason(smart will adapt linear in scaling up). But cubic retain smooth detail.

There might be some case that I don't know, so you should try it yourself to test what cause the situation.

Oh, and 2049x2049 might be the worst case that a map can be use in computer graphic. Try to let the map resolution in exponential of 2. e.g. 2048